Citizen participation in politics is a good place to begin our analysis of the Republic. Madison expected self-interested participation by citizens to be the foundation of the system. Political participation can be defined as any attempt to influence what the political system does. Madison’s theory expects everyone in the Republic to be self-interested, and citizens who become involved in politics to compel political leaders to respond to their interests.

We have seen how a star’s color or peak wavelength indicates its characteristic temperature near the stellar surface. But what about the temperature in the star’s deep interior? Intuitively, we expect this to be much higher than at the surface, but under what conditions does it become hot enough to allow for nuclear fusion to power the star’s luminosity? And how does it scale quantitatively with the overall stellar properties, such as mass, radius, and luminosity? To answer these questions, we identify two distinct considerations.

The post-main-sequence evolution of stars with higher initial mass (>8 solar masses) has some distinct differences from those of solar and intermediate-mass stars. We show how multiple-shell burning can lead to core-collapse supernovae, which are important in generating elements heavier than iron. Some supernovae can lead to the curious stellar endpoints of neutron stars and black holes.

What are the key physical properties we can aspire to know about a star? In this chapter we consider the properties of stars, identifying first what we can directly observe about a given star: position on the sky, apparent brightness, color/spectrum. When these observations are combined with a clear understanding of some basic physical principles, we can infer many of the key physical properties of stars. We also make a brief aside to discuss ways to get our heads around the enormous distances and timescales we encounter in astrophysics.

Radiation generated in the deep interior of a star undergoes a diffusion between multiple encounters with the stellar material before it can escape freely into space from the stellar surface. We define the optical depth by the number of mean free paths a photon takes from the center to the surface. This picture of photons undergoing a random walk through the stellar interior can be formalized in terms of a diffusion model for radiation transport in the interior.

Exoplanets are planets orbiting stars other than our sun. While some have now been detected (or confirmed) by direct imaging, most exoplanet detections have been made via two other more-indirect techniques, known as the radial-velocity and transit methods. These methods have analogs in the study of stellar binary systems, as outlined in Chapter 10. We explore the population of known exoplanets and how we must compensate for observational biases inherent in each of these techniques.

We start with some of the historical work on measuring distances to galaxies, leading to the Hubble (or Hubble–Lemaîe) law, a linear proportionality between recession velocity and and a galaxy’s distance, with a proportionality constant known as the Hubble constant. For more distant galaxies, it becomes increasingly difficult to detect and resolve even giant stars like Cepheid variables as individual objects, limiting their utility in testing the Hubble law to larger distances and redshifts. For much larger distances, an important alternative method is the Tully–Fisher relation.